Basic Linear Algebra Subprograms (BLAS) Library

The BLAS (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. There are three levels within the BLAS library:

• The Level 1 BLAS perform scalar, vector and vector-vector operations

• The Level 2 BLAS perform matrix-vector operations

• The Level 3 BLAS perform matrix-matrix operations

As the BLAS are efficient, portable, and widely available, they are commonly used in the development of high quality linear algebra software, LAPACK for example.

Popular BLAS (Basic Linear Algebra Subprograms) Implementations include:

• Intel's MKL (used in MKL DNN)
• OpenBLAS
• NetLib's BLAS
• BLAS++
• BLIS

Use

BLAS Libraries are used for the following:

• Speed up computations dealing with matrix and other operations
• Used within other optimized libraries such as MKL DNN
• Used within popular frameworks like TensorFlow

Level 1 BLAS routines

• SROTG - setup Givens rotation
• SROTMG - setup modified Givens rotation
• SROT - apply Givens rotation
• SROTM - apply modified Givens rotation
• SSWAP - swap x and y
• SSCAL - x = a*x
• SCOPY - copy x into y
• SAXPY - y = a*x + y
• SDOT - dot product
• SDSDOT - dot product with extended precision accumulation
• SNRM2 - Euclidean norm
• SCNRM2- Euclidean norm
• SASUM - sum of absolute values
• ISAMAX - index of max abs value
• DOUBLE
• DROTG - setup Givens rotation
• DROTMG - setup modified Givens rotation
• DROT - apply Givens rotation
• DROTM - apply modified Givens rotation
• DSWAP - swap x and y
• DSCAL - x = a*x
• DCOPY - copy x into y
• DAXPY - y = a*x + y
• DDOT - dot product
• DSDOT - dot product with extended precision accumulation
• DNRM2 - Euclidean norm
• DZNRM2 - Euclidean norm
• DASUM - sum of absolute values
• IDAMAX - index of max abs value
• CROTG - setup Givens rotation
• CSROT - apply Givens rotation
• CSWAP - swap x and y
• CSCAL - x = a*x
• CSSCAL - x = a*x
• CCOPY - copy x into y
• CAXPY - y = a*x + y
• CDOTU - dot product
• CDOTC - dot product, conjugating the first vector
• SCASUM - sum of absolute values
• ICAMAX - index of max abs value
• DOUBLE COMLPEX
• ZROTG - setup Givens rotation
• ZDROTF - apply Givens rotation
• ZSWAP - swap x and y
• ZSCAL - x = a*x
• ZDSCAL - x = a*x
• ZCOPY - copy x into y
• ZAXPY - y = a*x + y
• ZDOTU - dot product
• ZDOTC - dot product, conjugating the first vector
• DZASUM - sum of absolute values
• IZAMAX - index of max abs value

Level 2 BLAS routines

• SGEMV - matrix vector multiply
• SGBMV - banded matrix vector multiply
• SSYMV - symmetric matrix vector multiply
• SSBMV - symmetric banded matrix vector multiply
• SSPMV - symmetric packed matrix vector multiply
• STRMV - triangular matrix vector multiply
• STBMV - triangular banded matrix vector multiply
• STPMV - triangular packed matrix vector multiply
• STRSV - solving triangular matrix problems
• STBSV - solving triangular banded matrix problems
• STPSV - solving triangular packed matrix problems
• SGER - performs the rank 1 operation A := alphaxy' + A
• SSYR - performs the symmetric rank 1 operation A := alphaxx' + A
• SSPR - symmetric packed rank 1 operation A := alphaxx' + A
• SSYR2 - performs the symmetric rank 2 operation, A := alphaxy' + alphayx' + A
• SSPR2 - performs the symmetric packed rank 2 operation, A := alphaxy' + alphayx' + A
• DGEMV - matrix vector multiply
• DGBMV - banded matrix vector multiply
• DSYMV - symmetric matrix vector multiply
• DSBMV - symmetric banded matrix vector multiply
• DSPMV - symmetric packed matrix vector multiply
• DTRMV - triangular matrix vector multiply
• DTBMV - triangular banded matrix vector multiply
• DTPMV - triangular packed matrix vector multiply
• DTRSV - solving triangular matrix problems
• DTBSV - solving triangular banded matrix problems
• DTPSV - solving triangular packed matrix problems
• DGER - performs the rank 1 operation A := alphaxy' + A
• DSYR - performs the symmetric rank 1 operation A := alphaxx' + A
• DSPR - symmetric packed rank 1 operation A := alphaxx' + A
• DSYR2 - performs the symmetric rank 2 operation, A := alphaxy' + alphayx' + A
• DSPR2 - performs the symmetric packed rank 2 operation, A := alphaxy' + alphayx' + A
• CGEMV - matrix vector multiply
• CGBMV - banded matrix vector multiply
• CHEMV - hermitian matrix vector multiply
• CHBMV - hermitian banded matrix vector multiply
• CHPMV - hermitian packed matrix vector multiply
• CTRMV - triangular matrix vector multiply
• CTBMV - triangular banded matrix vector multiply
• CTPMV - triangular packed matrix vector multiply
• CTRSV - solving triangular matrix problems
• CTBSV - solving triangular banded matrix problems
• CTPSV - solving triangular packed matrix problems
• CGERU - performs the rank 1 operation A := alphaxy' + A
• CGERC - performs the rank 1 operation A := alphaxconjg( y' ) + A
• CHER - hermitian rank 1 operation A := alphaxconjg(x') + A
• CHPR - hermitian packed rank 1 operation A := alphaxconjg( x' ) + A
• CHER2 - hermitian rank 2 operation
• CHPR2 - hermitian packed rank 2 operation
• ZGEMV - matrix vector multiply
• ZGBMV - banded matrix vector multiply
• ZHEMV - hermitian matrix vector multiply
• ZHBMV - hermitian banded matrix vector multiply
• ZHPMV - hermitian packed matrix vector multiply
• ZTRMV - triangular matrix vector multiply
• ZTBMV - triangular banded matrix vector multiply
• ZTPMV - triangular packed matrix vector multiply
• ZTRSV - solving triangular matrix problems
• ZTBSV - solving triangular banded matrix problems
• ZTPSV - solving triangular packed matrix problems
• ZGERU - performs the rank 1 operation A := alphaxy' + A
• ZGERC - performs the rank 1 operation A := alphaxconjg( y' ) + A
• ZHER - hermitian rank 1 operation A := alphaxconjg(x') + A
• ZHPR - hermitian packed rank 1 operation A := alphaxconjg( x' ) + A
• ZHER2 - hermitian rank 2 operation
• ZHPR2 - hermitian packed rank 2 operation

Level 3 BLAS routines

• SGEMM - matrix matrix multiply
• SSYMM - symmetric matrix matrix multiply
• SSYRK - symmetric rank-k update to a matrix
• SSYR2K - symmetric rank-2k update to a matrix
• STRMM - triangular matrix matrix multiply
• STRSM - solving triangular matrix with multiple right hand sides
• DGEMM - matrix matrix multiply
• DSYMM - symmetric matrix matrix multiply
• DSYRK - symmetric rank-k update to a matrix
• DSYR2K - symmetric rank-2k update to a matrix
• DTRMM - triangular matrix matrix multiply
• DTRSM - solving triangular matrix with multiple right hand sides
• CGEMM - matrix matrix multiply
• CSYMM - symmetric matrix matrix multiply
• CHEMM - hermitian matrix matrix multiply
• CSYRK - symmetric rank-k update to a matrix
• CHERK - hermitian rank-k update to a matrix
• CSYR2K - symmetric rank-2k update to a matrix
• CHER2K - hermitian rank-2k update to a matrix
• CTRMM - triangular matrix matrix multiply
• CTRSM - solving triangular matrix with multiple right hand sides
• ZGEMM - matrix matrix multiply
• ZSYMM - symmetric matrix matrix multiply
• ZHEMM - hermitian matrix matrix multiply
• ZSYRK - symmetric rank-k update to a matrix
• ZHERK - hermitian rank-k update to a matrix
• ZSYR2K - symmetric rank-2k update to a matrix
• ZHER2K - hermitian rank-2k update to a matrix
• ZTRMM - triangular matrix matrix multiply
• ZTRSM - solving triangular matrix with multiple right hand sides